Prime specialization in genus 0

For a prime polynomial , a classical conjecture predicts how often has prime values. For a finite field and a prime polynomial , the natural analogue of this conjecture (a prediction for how often takes prime values on ) is not generally true when is a polynomial in ( the characteristic of ). The explanation rests on a new global obstruction which can be measured by an appropriate average of the nonzero Möbius values as varies. We prove the surprising fact that this ``Möbius average,' which can be defined without reference to any conjectures, has a periodic behavior governed by the geometry of the plane curve .

The periodic Möbius average behavior implies in specific examples that a polynomial in does not take prime values as often as analogies with suggest, and it leads to a modified conjecture for how often prime values occur.

     

One‐ or Two‐Electron Transfer? The Ambiguous Nature of the Discharge Products in Sodium–Oxygen Batteries

Rechargeable lithium–oxygen and sodium–oxygen cells have been considered as challenging concepts for next‐generation batteries, both scientifically and technologically. Whereas in the case of non‐aqueous Li/O₂ batteries, the occurring cell reaction has been unequivocally determined (Li₂O₂ formation), the situation is much less clear in the case of non‐aqueous Na/O₂ cells. Two discharge products, with almost equal free enthalpies of formation but different numbers of transferred electrons and completely different kinetics, appear to compete, namely NaO₂ and Na₂O₂. Cells forming either the superoxide or the peroxide have been reported, but it is unclear how the cell reaction can be influenced for selective one‐ or two‐electron transfer to occur. In this Minireview, we summarize available data, discuss important control parameters, and offer perspectives for further research. Water and proton sources appear to play major roles.     

Synthesis of a Ferrolite: A Zeolitic All‐Iron Framework

Crystals of the first sodalite‐type zeolite containing an all‐iron framework, a ferrolite, Ba₈(Fe₁₂O₂₄)Na_y(OH)₆?x H₂O, were synthesized using the hydroflux method in nearly quantitative yield. Ba₈(Fe₁₂O₂₄)Na_y(OH)₆?x H₂O crystallizes in the cubic space group with a=10.0476(1) Å. Slightly distorted FeO₄ tetrahedra are linked to form Fe₄O₄ and Fe₆O₆ rings, which in turn yield channels and internal cavities that are characteristic of the sodalite structure. Barium, sodium, and hydroxide ions and water molecules are found in the channels and provide charge balance. Magnetic measurements indicate that the ferrolite exhibits magnetic order up to at least 700 K, with the field‐cooled and zero‐field‐cooled curves diverging. Analysis of the ⁵⁷Fe Mössbauer spectra revealed two spectral components that have equal spectral areas, indicating the presence of two subsets of iron centers in the structure. Dehydrated versions of the ferrolite were also prepared by heating the sample.     

Student Perceptions of a Summer Ventures in Science and Mathematics Camp Experience

“As the world becomes increasingly technological, the value of (the ideas and skills of its population) will be determined in no small measure by the effectiveness of science, technology, engineering, and mathematics (STEM) education in the United States” and “STEM education will determine whether the United States will remain a leader among nations and whether we will be able to solve immense challenges in such areas as energy, health, environmental protection, and national security” (President's Council of Advisors on Science and Technology, 2010, p. vii). Research on the effectiveness of STEM‐focused school and other learning experiences (e.g., short‐term camps) on student attitudes and performance outcomes is sparse. In this study, we documented the influence of an intensive STEM summer program on high school students’ attitudes toward STEM concepts and interests in STEM careers. Attending the summer program was associated with gains on students’ attitudes toward some aspects of STEM as well as specific career interests. Notably, students reported statistically significant views of important aspects of STEM and their attitudes toward science and mathematics were more positive than their attitudes about engineering and technology.     

A general and efficient 2-amination of pyridines and quinolines

Pyridine N-oxides were converted to 2-aminopyridines in a one-pot fashion using Ts2O-t-BuNH2 followed by in situ deprotection with TFA. The amination proceeded in high yields, excellent 2-/4-selectivity, and with good functional group compatibility. 2-Amino (iso)quinolines were also obtained in the same manner. Combined with the simple oxidation of pyridines to pyridine N-oxides, this method provides a general and efficient way for amination of 2-unsubstituted pyridines.     

High-sensitivity laser-based ultrasonic C-scan system for materials inspection

A beam-steering C-scan system for laser generation and detection of ultrasound in opaque solids has been developed. For ultrasound detection, the system uses a confocal Fabry-Perot interferometer that is stabilized at its high-sensitivity point by implementing a novel procedure that does not require a reference beam. This stabilization procedure effectively compensates for slowly varying (up to 2 Hz) disturbances and, more important, for any change in the interferometer illumination conditions while probing different scanning points. For the latter reason, the proposed stabilization appears to be more effective than previous approaches for high-sensitivity ultrasound detection in beamsteering scans. Noise performance and sensitivity limit of the system are evaluated. Ultrasonic echoes are detected in aluminum samples having optically rough surfaces with single-pulse generation signal-to-noise ratios on the order of 20 dB. A C-scan inspection is performed where a known defect in the test piece is successfully detected by time-of-flight gating of the ultrasonic signals.     

Complexation and redox chemistry of neptunium,plutonium and americium with a hydroxylaminato ligand

There is significant interest in ligands that can stabilize actinide ions in oxidation states that can be exploited to chemically differentiate 5f and 4f elements. Applications range from developing large-scale actinide separation strategies for nuclear industry processing to carrying out analytical studies that support environmental monitoring and remediation efforts. Here, we report syntheses and characterization of Np(iv), Pu(iv) and Am(iii) complexes with N-tert-butyl-N-(pyridin-2-yl)hydroxylaminato, [2-(^tBuNO)py]⁻(interchangeable hereafter with [(^tBuNO)py]⁻), a ligand which was previously found to impart remarkable stability to cerium in the +4 oxidation state. An[(^tBuNO)py]₄ (An = Pu, 1; Np, 2) have been synthesized, characterized by X-ray diffraction, X-ray absorption, ¹H NMR and UV-vis-NIR spectroscopies, and cyclic voltammetry, along with computational modeling and analysis. In the case of Pu, oxidation of Pu(iii) to Pu(iv) was observed upon complexation with the [(^tBuNO)py]⁻ ligand. The Pu complex 1 and Np complex 2 were also isolated directly from Pu(iv) and Np(iv) precursors. Electrochemical measurements indicate that a Pu(iii) species can be accessed upon one-electron reduction of 1 with a large negative reduction potential (E_1/2 = −2.26 V vs. Fc^+/0). Applying oxidation potentials to 1 and 2 resulted in ligand-centered electron transfer reactions, which is different from the previously reported redox chemistry of U^IV[(^tBuNO)py]₄ that revealed a stable U(v) product. Treatment of an anhydrous Am(iii) precursor with the [(^tBuNO)py]⁻ ligand did not result in oxidation to Am(iv). Instead, the dimeric complex [Am^III(μ₂-(^tBuNO)py)((^tBuNO)py)₂]₂ (3) was isolated. Complex 3 is a rare example of a structurally characterized non-aqueous Am-containing molecular complex prepared using inert atmosphere techniques. Predicted redox potentials from density functional theory calculations show a trivalent accessibility trend of U(iii) < Np(iii) < Pu(iii) and that the higher oxidation states of actinides (i.e., +5 for Np and Pu and +4 for Am) are not stabilized by [2-(^tBuNO)py]⁻, in good agreement with experimental observations.

The coordination modes and electronic properties of a strongly coordinating hydroxylaminato ligand with Np, Pu and Am were investigated.Complexes were characterized by a range of experimental and computational techniques.     

A Dodecagonal Quasicrystalline Chalcogenide

Diffractograms with twelvefold rotational symmetry (depicted on the right) were obtained from the first quasicrystalline chalcogenide Ta_1.6Te. This compound was prepared on a preparative scale by the reduction of TaTe₂ with tantalum below 1870 K. This tantalum-rich telluride, which is the first stable dodecagonal phase, has enabled an in-depth investigation of this unusual state of ordering.